College Physics: A Strategic Approach

Randall D. Knight, Brian Jones, Stuart Field

Chapter 5

Applying Newton's Laws - all with Video Answers

Educators

+ 5 more educators

Chapter Questions

Problem 1

The three ropes in Figure P5.1 are tied to a small, very light ring. Two of the ropes are anchored to walls at right angles, and the third rope pulls as shown. What are $T_{1}$ and $T_{2}$, the magnitudes of the tension forces in the first two ropes?

Sachin Rao

Sachin Rao

Numerade Educator

Problem 2

In the sport of parasailing, a person is attached to a rope being pulled by a boat while hanging from a parachute-like sail. A rider is towed at a constant speed by a rope that is at an angle of $15^{\circ}$ from horizontal. The tension in the rope is $2300 \mathrm{N}$. The force of the sail on the rider is $30^{\circ}$ from horizontal. What is the weight of the rider?

Sachin Rao

Numerade Educator

Problem 3

In the Skycoaster amusement park ride, riders are suspended from a tower by a long cable. A second cable then lifts them until they reach the starting position indicated in Figure $\mathrm{P} 5.3$. The lifting cable is then released, and the riders swing down the circular arc shown. If the four riders have a total mass of $270 \mathrm{kg}$, what are the tensions in the two cables just before release?

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 4

A construction crew would like to support a 1000 kg steel beam with two angled ropes as shown in Figure $\mathrm{P} 5.4$ Their rope can support a maximum tension of $5600 \mathrm{N}$. Is this rope strong enough to do the job?

Vishal Gupta

Numerade Educator

Problem 5

When you bend your knee, the quadriceps muscle is stretched. This increases the tension in the quadriceps tendon attached to your kneecap (patella), which, in turn, increases the tension in the patella tendon that attaches your kneecap to your lower leg bone (tibia). Simultaneously, the end of your upper leg bone (femur) pushes outward on the patella. Figure $\mathrm{P} 5.5$ shows how these parts of a knee joint are arranged. What size force does the femur exert on the kneecap if the tendons are oriented as in the figure and the tension in each tendon is $60 \mathrm{N} ?$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 6

An early submersible craft for deep-sea exploration was raised and lowered by a cable from a ship. When the craft was stationary, the tension in the cable was $6000 \mathrm{N}$. When the craft was lowered or raised at a steady rate, the motion through the water added an $1800 \mathrm{N}$ drag force.
a. What was the tension in the cable when the craft was being lowered to the seafloor?
b. What was the tension in the cable when the craft was being raised from the seafloor?

Sachin Rao

Numerade Educator

Problem 7

Bethany, who weighs $560 \mathrm{N}$, lies in a hammock suspended by ropes tied to two trees. One rope makes an angle of $45^{\circ}$ with the ground; the other makes an angle of $30^{\circ} .$ Find the tension in each of the ropes.

Sachin Rao

Numerade Educator

Problem 8

$\mathrm{A} 65 \mathrm{kg}$ student is walking on a slackline, a length of webbing stretched between two trees. The line stretches and so has a noticeable sag, as shown in Figure $\mathrm{P} 5.8$. At the point where his foot touches the line, the rope applies a tension force in each direction, as shown. What is the tension in the line?

Sachin Rao

Numerade Educator

Problem 9

In the winter sport of curling, two teams alternate sliding $20 \mathrm{kg}$ stones on an icy surface in an attempt to end up with the stone closest to the center of a target painted on the ice. During one turn, a player releases a stone that travels $27.9 \mathrm{m}$ before coming to rest. The friction force acting on the stone is $2.0 \mathrm{N}$. What was the speed of the stone when the player released it?

Supratim Pal

Numerade Educator

Problem 10

The forces in Figure $\mathrm{P} 5.10$ are acting on a $2.0 \mathrm{kg}$ object. What is $a_{x},$ the $x$ -component of the object's acceleration?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 11

The forces in Figure $\mathrm{P} 5.11$ are acting on a $2.0 \mathrm{kg}$ object. Find the values of $a_{x}$ and $a_{y},$ the $x$ - and $y$ -components of the object's acceleration.

Sachin Rao

Numerade Educator

Problem 12

A horizontal rope is tied to a $50 \mathrm{kg}$ box on frictionless ice. What is the tension in the rope if
a. The box is at rest?
b. The box moves at a steady $5.0 \mathrm{m} / \mathrm{s} ?$
c. The box has $v_{x}=5.0 \mathrm{m} / \mathrm{s}$ and $a_{x}=5.0 \mathrm{m} / \mathrm{s}^{2} ?$

Sachin Rao

Numerade Educator

Problem 13

The acceleration of a baseball pitcher's hand as he delivers a pitch is extreme. For a professional player, this acceleration phase lasts only 50 ms, during which the ball's speed increases from 0 to about $90 \mathrm{mph},$ or $40 \mathrm{m} / \mathrm{s}$. What is the force of the pitcher's hand on the $0.145 \mathrm{kg}$ ball during this acceleration phase?

Sachin Rao

Numerade Educator

Problem 14

In a head-on collision, a car stops in 0.10 s from a speed of $14 \mathrm{m} / \mathrm{s} .$ The driver has a mass of $70 \mathrm{kg},$ and is, fortunately, tightly strapped into his seat. What force is applied to the driver by his seat belt during that fraction of a second?

Sachin Rao

Numerade Educator

Problem 15

An astronaut's weight on earth is $800 \mathrm{N}$. What is his weight on Mars, where $g=3.76 \mathrm{m} / \mathrm{s}^{2} ?$

Sachin Rao

Numerade Educator

Problem 16

A woman has a mass of $55.0 \mathrm{kg}$.
a. What is her weight on earth?
b. What are her mass and her weight on the moon, where $g=1.62 \mathrm{m} / \mathrm{s}^{2} ?$

Sachin Rao

Numerade Educator

Problem 17

The acceleration of the spacecraft in which the Apollo astronauts took off from the moon was $3.4 \mathrm{m} / \mathrm{s}^{2} .$ On the moon, $g=1.6 \mathrm{m} / \mathrm{s}^{2} .$ What was the apparent weight of a $75 \mathrm{kg}$ astronaut during takeoff?

Narayan Hari

Numerade Educator

Problem 18

a. How much force does an $80 \mathrm{kg}$ astronaut exert on his chair while sitting at rest on the launch pad?
b. How much force does the astronaut exert on his chair
while accelerating straight up at $10 \mathrm{m} / \mathrm{s}^{2} ?$

Sachin Rao

Numerade Educator

Problem 19

It takes the elevator in a skyscraper $4.0 \mathrm{s}$ to reach its cruising speed of $10 \mathrm{m} / \mathrm{s}$. A $60 \mathrm{kg}$ passenger gets aboard on the ground floor. What is the passenger's apparent weight
a. Before the elevator starts moving?
b. While the elevator is speeding up?
c. After the elevator reaches its cruising speed?

Sachin Rao

Numerade Educator

Problem 20

Riders on the Power Tower are launched skyward with an acceleration of $4 g,$ after which they experience a a period of free fall. What is a $60 \mathrm{kg}$ rider's apparent weight
a. During the launch?
b. During the period of free fall?

Sachin Rao

Numerade Educator

Problem 21

Zach, whose mass is $80 \mathrm{kg}$, is in an elevator descending at $10 \mathrm{m} / \mathrm{s}$. The elevator takes 3.0 s to brake to a stop at the first floor.
a. What is Zach's apparent weight before the elevator starts braking?
b. What is Zach's apparent weight while the elevator is braking?

Sachin Rao

Numerade Educator

Problem 22

An astronaut lifts off in a rocket from the surface of the moon, where $g=1.6 \mathrm{m} / \mathrm{s}^{2} .$ What vertical acceleration should his rocket have so that his apparent weight is equal to his true weight on earth?

Sachin Rao

Numerade Educator

Problem 23

Figure $\mathrm{P} 5.23$ shows the velocity graph of a $75 \mathrm{kg}$ passenger in an elevator. What is the passenger's apparent weight at $t=1.0$ s? At 5.0 s? At 9.0 s?

Sachin Rao

Numerade Educator

Problem 24

Mountain goats can easily scale slopes angled at $60^{\circ}$ from horizontal. What are the normal force and the static friction force acting on a mountain goat that weighs $900 \mathrm{N}$ and is standing on such a slope?

Sachin Rao

Numerade Educator

Problem 25

$\mathrm{A} 23 \mathrm{kg}$ child goes down a straight slide inclined $38^{\circ}$ above horizontal. The child is acted on by his weight, the normal force from the slide, and kinetic friction.
a. Draw a free-body diagram of the child.
b. How large is the normal force of the slide on the child?

Sachin Rao

Numerade Educator

Problem 26

A crate pushed along the floor with velocity $\vec{v}_{\mathrm{i}}$ slides a distance $d$ after the pushing force is removed.
a. If the mass of the crate is doubled but the initial velocity is not changed, what distance does the crate slide before stopping? Explain.
b. If the initial velocity of the crate is doubled to $2 \vec{v}_{\mathrm{i}}$ but the mass is not changed, what distance does the crate slide before stopping? Explain.

Sachin Rao

Numerade Educator

Problem 27

Two workers are sliding a $300 \mathrm{kg}$ crate across the floor. One worker pushes forward on the crate with a force of $380 \mathrm{N}$ while the other pulls in the same direction with a force of $350 \mathrm{N}$ using a rope connected to the crate. Both forces are horizontal, and the crate slides with a constant speed. What is the crate's coefficient of kinetic friction on the floor?

Sachin Rao

Numerade Educator

Problem 28

A 4000 kg truck is parked on a 7.0 " slope. How big is the friction force on the truck?

Ankur S

Numerade Educator

Problem 28

$\mathrm{A} 4000 \mathrm{kg}$ truck is parked on a $7.0^{\circ}$ slope. How big is the friction force on the truck?

Sachin Rao

Numerade Educator

Problem 29

$\mathrm{A} 1000 \mathrm{kg}$ car traveling at a speed of $40 \mathrm{m} / \mathrm{s}$ skids to a halt on wet concrete where $\mu_{\mathrm{k}}=0.60 .$ How long are the skid marks?

Sachin Rao

Numerade Educator

Problem 30

A dump truck, whose bed is made of steel, holds an old steel watering trough. The bed of the truck is slowly raised until the trough begins to slide. What is the acceleration of the trough as it slides down the truck bed?

Supratim Pal

Numerade Educator

Problem 31

A $10 \mathrm{kg}$ crate is placed on a horizontal conveyor belt. The materials are such that $\mu_{\mathrm{s}}=0.50$ and $\mu_{\mathrm{k}}=0.30$
a. Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed.
b. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up.
c. What is the maximum acceleration the belt can have without the crate slipping? If the acceleration of the belt exceeds the value determined in part c, what is the acceleration of the crate?

Sachin Rao

Numerade Educator

Problem 32

It is friction that provides the force for a car to accelerate, so for high-performance cars the factor that limits acceleration isn't the engine; it's the tires. For typical rubber-on-concrete friction, what is the shortest time in which a car could accelerate from 0 to 60 mph?

Sachin Rao

Numerade Educator

Problem 33

The rolling resistance for steel on steel is quite low; the coefficient of rolling friction is typically $\mu_{\mathrm{r}}=0.002 .$ Suppose a 180,000 kg locomotive is rolling at $10 \mathrm{m} / \mathrm{s}$ (just over $20 \mathrm{mph}$ ) on level rails. If the engineer disengages the engine, how much time will it take the locomotive to coast to a stop? How far will the locomotive move during this time?

Sachin Rao

Numerade Educator

Problem 34

A vendor at the local art fair ties her tent to the concrete-filled coffee can shown in Figure $\mathrm{P} 5.34 .$ A stiff breeze comes up and the string becomes taut. What is the maximum value that the string tension can have before the can slips? The coefficient of static friction between the can and the ground is $0.60 .$

Sachin Rao

Numerade Educator

Problem 35

Oceanographers use submerged sonar systems, towed by a cable from a ship, to map the ocean floor. In addition to their downward weight, there are buoyant forces and forces from the flowing water that allow them to travel in a horizontal path. One such submersible has a cross-section area of $1.3 \mathrm{m}^{2},$ a drag coefficient of $1.2,$ and, when towed at $5.1 \mathrm{m} / \mathrm{s},$ the tow cable makes an angle of $30^{\circ}$ with the horizontal. What is the tension in the cable?

Sachin Rao

Numerade Educator

Problem 36

At its widest point, the diameter of a bottlenose dolphin is $0.50 \mathrm{m} .$ Bottlenose dolphins are particularly sleek, having a drag coefficient of only about 0.090 .
a. What is the drag force acting on such a dolphin swimming at $7.5 \mathrm{m} / \mathrm{s} ?$
b. Using the dolphin's diameter as its characteristic length, what is the Reynolds number as it swims at this speed in $20^{\circ} \mathrm{C}$ water?

Supratim Pal

Numerade Educator

Problem 37

The most dangerous particles in polluted air are those with diameters less than $2.5 \mu \mathrm{m}$ because they can penetrate deeply into the lungs. A 15 -cm-tall closed container holds a sample of polluted air containing many spherical particles with a diameter of $2.5 \mu \mathrm{m}$ and a mass of $1.4 \times 10^{-14} \mathrm{kg} .$ How long does it take for all of the particles to settle to the bottom of the container?

Narayan Hari

Numerade Educator

Problem 38

Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Suppose a $60 \mathrm{kg}$ runner completes a $5.0 \mathrm{km}$ race in 18 minutes. Use the crosssection area estimate of Example 5.15 to determine the drag force on the runner during the race. What is this force as a fraction of the runner's weight?

Sachin Rao

Numerade Educator

Problem 39

What is the magnitude of the acceleration of a skydiver who is currently falling at one-half his eventual terminal speed?

Sachin Rao

Numerade Educator

Problem 40

The air is less dense at higher elevations, so skydivers reach a high terminal speed. The highest recorded speed for a skydiver was achieved in a jump from a height of $39,000 \mathrm{m}$. At this elevation, the density of the air is only $4.3 \%$ of the surface density. Use the data from Example 5.15 to estimate the terminal speed of a skydiver at this elevation.

Jerrah Biggerstaff

Jerrah Biggerstaff

Numerade Educator

Problem 41

A $1000 \mathrm{kg}$ car pushes a $2000 \mathrm{kg}$ truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push backward against the ground with a force of $4500 \mathrm{N}.$
a. What is the magnitude of the force of the car on the truck?
b. What is the magnitude of the force of the truck on the car?

Sachin Rao

Numerade Educator

Problem 42

$\mathrm{A} 2200 \mathrm{kg}$ truck has put its front bumper against the rear bumper of a $2400 \mathrm{kg}$ SUV to give it a push. With the engine at full power and good tires on good pavement, the maximum forward force on the truck is $18,000 \mathrm{N}$.
a. What is the maximum possible acceleration the truck can give the SUV?
b. At this acceleration, what is the force of the SUV's bumper on the truck's bumper?

Sachin Rao

Numerade Educator

Problem 43

Blocks with masses of $1.0 \mathrm{kg}, 2.0 \mathrm{kg},$ and $3.0 \mathrm{kg}$ are lined up in a row on a frictionless table. All three are pushed forward by a $12 \mathrm{N}$ force applied to the $1.0 \mathrm{kg}$ block. How much force does the $2.0 \mathrm{kg}$ block exert on (a) the $3.0 \mathrm{kg}$ block and (b) the $1.0 \mathrm{kg}$ block?

Sachin Rao

Numerade Educator

Problem 44

What is the tension in the rope of Figure $\mathrm{P} 5.44 ?$

Mukesh Devi

Numerade Educator

Problem 45

A house painter uses the chair-and-pulley arrangement of Figure P5.45 to lift himself up the side of a house. The painter's mass is $70 \mathrm{kg}$ and the chair's mass is $10 \mathrm{kg}$. If the painter is at rest, what is the tension in the rope?

Sachin Rao

Numerade Educator

Problem 46

Figure P5.46 shows two $1.00 \mathrm{kg}$ blocks connected by a rope. A second rope hangs beneath the lower block. Both ropes have a mass of 250 g. The entire assembly is accelerated upward at $3.00 \mathrm{m} / \mathrm{s}^{2}$ by force $\vec{F}$
a. What is $F ?$
b. What is the tension at the top end of rope $1 ?$
c. What is the tension at the bottom end of rope $1 ?$
d. What is the tension at the top end of rope $2 ?$

Sachin Rao

Numerade Educator

Problem 47

Each of 100 identical blocks sitting on a frictionless surface is connected to the next block by a massless string. The first block is pulled with a force of $100 \mathrm{N}$.
a. What is the tension in the string connecting block 100 to block 99?
b. What is the tension in the string connecting block 50 to block $51 ?$

Sachin Rao

Numerade Educator

Problem 48

A Jeep is stuck in the mud. The driver has a winch that can pull on its cable with a force of $40,000 \mathrm{N}$. The driver loops the cable through a pulley attached to a tree, then attaches the end of the cable to his Jeep, as shown in Figure $\mathrm{P} 5.48 .$ What is the maximum force that can be exerted on the Jeep by this cable arrangement?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 49

A 500 kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. Bob's rope pulls to the left, $15^{\circ}$ below horizontal, with $500 \mathrm{N}$ of tension. Ellen's rope pulls toward the right, $25^{\circ}$ below horizontal.
a. What tension must Ellen maintain in her rope to keep the piano descending vertically at constant speed?
b. What is the tension in the vertical main cable supporting the piano?

Sachin Rao

Numerade Educator

Problem 50

Dana has a sports medal suspended by a long ribbon from her rearview mirror. As she accelerates onto the highway, she notices that the medal is hanging at an angle of $10^{\circ}$ from the vertical.
a. Does the medal lean toward or away from the windshield? Explain.
b. What is her acceleration?

Sachin Rao

Numerade Educator

Problem 51

Figure P5.51 shows the velocity graph of a $2.0 \mathrm{kg}$ object as it moves along the $x$ -axis. What is the net force acting on this object at $t=1$ s? $\mathrm{At} 4 \mathrm{s} ?$ At $7 \mathrm{s} ?$

Sachin Rao

Numerade Educator

Problem 52

Your forehead can withstand a force of about $6.0 \mathrm{kN}$ before
fracturing, while your cheekbone can only withstand about $1.3 \mathrm{kN}$.
a. If a 140 g baseball strikes your head at $30 \mathrm{m} / \mathrm{s}$ and stops in $0.0015 \mathrm{s},$ what is the magnitude of the ball's acceleration?
b. What is the magnitude of the force that stops the baseball?
c. What force does the baseball apply to your head? Explain.
d. Are you in danger of a fracture if the ball hits you in the forehead? In the cheek?

Sachin Rao

Numerade Educator

Problem 53

$\mathrm{A} 50 \mathrm{kg}$ box hangs from a rope. What is the tension in the rope if
a. The box is at rest?
b. The box has $v_{y}=5.0 \mathrm{m} / \mathrm{s}$ and is speeding up at $5.0 \mathrm{m} / \mathrm{s}^{2} ?$

Sachin Rao

Numerade Educator

Problem 54

Scientists have studied how snakes grip and climb ropes. In one study, they found that an important characteristic of a rope is its "compliance"that is, how easily the rope, while under tension, can be flexed. Figure P5.54 shows how scientists measured a rope's compliance by attaching it to two strings, each supporting an identical mass $m$. The strings contort the rope so that its middle section lies at angle $\theta$. For $\theta=30^{\circ}$ and $m=100 \mathrm{g},$ what are the tensions $T_{1}$ and $T_{2}$ in the upper and middle parts of the rope?

Sachin Rao

Numerade Educator

Problem 55

A $50 \mathrm{kg}$ box hangs from a rope. What is the tension in the rope if
a. The box moves up at a steady $5.0 \mathrm{m} / \mathrm{s} ?$
b. The box has $v_{y}=5.0 \mathrm{m} / \mathrm{s}$ and is slowing down at $5.0 \mathrm{m} / \mathrm{s}^{2} ?$

Sachin Rao

Numerade Educator

Problem 56

A fisherman has caught a very large, $5.0 \mathrm{kg}$ fish from a dock that is $2.0 \mathrm{m}$ above the water. He is using lightweight fishing line that will break under a tension of $54 \mathrm{N}$ or more. He is eager to get the fish to the dock in the shortest possible time. If the fish is at rest at the water's surface, what's the least amount of time in which the fisherman can raise the fish to the dock without losing it?

Sachin Rao

Numerade Educator

Problem 57

Riders on the Tower of Doom, an amusement park ride, experience $2.0 \mathrm{s}$ of free fall, after which they are slowed to a stop in 0.50 s. What is a 65 kg rider's apparent weight as the ride is coming to rest? By what factor does this exceed her actual weight?

Sachin Rao

Numerade Educator

Problem 58

Just after launch, the space shuttle takes 8.0 s to reach a speed of $160 \mathrm{km} / \mathrm{h}$. During this phase, what is the apparent weight of a $72 \mathrm{kg}$ astronaut?

Sachin Rao

Numerade Educator

Problem 59

Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a "crumple zone" in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about $1 \mathrm{m}$ as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton's first law!) until hitting the dashboard or windshield, as we saw in Figure $4.2 .$ These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about $5 \mathrm{mm}$
a. A $60 \mathrm{kg}$ person is in a head-on collision. The car's speed at impact is $15 \mathrm{m} / \mathrm{s}$. Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.
b. Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag.
c. How do these two forces compare to the person's weight?

Jerrah Biggerstaff

Jerrah Biggerstaff

Numerade Educator

Problem 60

Corey, whose mass is $95 \mathrm{kg}$, stands on a bathroom scale in an elevator. The scale reads $830 \mathrm{N}$ for the first $3.0 \mathrm{s}$ after the
elevator starts to move, then $930 \mathrm{N}$ for the next $3.0 \mathrm{s}$. What is the elevator's velocity $6.0 \mathrm{s}$ after starting?

Sachin Rao

Numerade Educator

Problem 61

A 20,000 kg rocket has a rocket motor that generates $3.0 \times 10^{5} \mathrm{N}$ of thrust.
a. What is the rocket's initial upward acceleration?
b. At an altitude of $5.0 \mathrm{km}$ the rocket's acceleration has increased to $6.0 \mathrm{m} / \mathrm{s}^{2} .$ What mass of fuel has it burned?

Sachin Rao

Numerade Educator

Problem 62

You've always wondered about the acceleration of the elevators: in the 101 -story-tall Empire State Building. One day, while visiting New York, you take your bathroom scale into the elevator and stand on it. The scale reads $150 \mathrm{lb}$ as the door closes. The reading varies between $120 \mathrm{lb}$ and $170 \mathrm{lb}$ as the elevator travels $101 \mathrm{floors}$.
a. What is the magnitude of the acceleration as the elevator starts upward?
b. What is the magnitude of the acceleration as the elevator brakes to a stop?

Sachin Rao

Numerade Educator

Problem 63

A 23 kg child goes down a straight slide inclined $38^{\circ}$ above horizontal. The child is acted on by his weight, the normal force from the slide, kinetic friction, and a horizontal rope exerting a $30 \mathrm{N}$ force as shown in Figure P5.63. How large is the normal force of the slide on the child?

Sachin Rao

Numerade Educator

Problem 64

An impala is an African antelope capable of a remarkable vertical leap. In one recorded leap, a 45 kg impala went into a deep crouch, pushed straight up for 0.21 s, and reached a height of $2.5 \mathrm{m}$ above the ground. To achieve this vertical leap, with what force did the impala push down on the ground? What is the ratio of this force to the antelope's weight?

Sachin Rao

Numerade Educator

Problem 65

Josh starts his sled at the top of a $3.0-\mathrm{m}$ -high hill that has a constant slope of $25^{\circ} .$ After reaching the bottom, he slides across a horizontal patch of snow. Ignore friction on the hill, but assume that the coefficient of kinetic friction between his sled and the horizontal patch of snow is $0.050 .$ How far from the base of the hill does he end up?

Sachin Rao

Numerade Educator

Problem 66

The standing vertical jump is a good test of an athlete's strength and fitness. The athlete goes into a deep crouch, then extends his legs rapidly; when his legs are fully extended, he leaves the ground and rises to his highest height. It is the force of the ground on the athlete during the extension phase that accelerates the athlete to the final speed with which he leaves the ground. A good jumper can exert a force on the ground equal to twice his weight. If his crouch is $60 \mathrm{cm}$ deep, how far off the ground does he rise?

Nicholas Mogoi

Numerade Educator

Problem 67

$\mathrm{A}$ 70 kg bicyclist is coasting down a long hill with a $3.5^{\circ}$ slope. He's moving quite rapidly, so air drag is important. His cross-section area is $0.32 \mathrm{m}^{2}$ and his drag coefficient is 0.88 What speed does he eventually reach, in mph?

Sachin Rao

Numerade Educator

Problem 68

Many birds can attain very high speeds when diving. Using radar, scientists measured the altitude of a barn swallow in a vertical dive; it dropped $208 \mathrm{m}$ in $3.0 \mathrm{s}$. The mass of the swallow was estimated to be $0.018 \mathrm{kg}$, and its cross-section area as $5.6 \times 10^{-4} \mathrm{m}^{2}$. What was the drag coefficient for this swallow as it dove?

Paul Gabriel

Numerade Educator

Problem 69

The drag on a pitched baseball can be surprisingly large. Suppose a 145 g baseball with a diameter of $7.4 \mathrm{cm}$ has an initial speed of $40.2 \mathrm{m} / \mathrm{s}(90 \mathrm{mph})$
a. What is the magnitude of the ball's acceleration due to the drag force?
b. If the ball had this same acceleration during its entire $18.4 \mathrm{m}$ trajectory, what would its final speed be?

Donald Albin

Numerade Educator

Problem 70

Small particulates can be removed from the emissions of a coalfired power plant by electrostatic precipitation. The particles are given a small electric charge that draws them toward oppositely charged plates, where they stick. Consider a spherical particulate with a diameter of $1.0 \mu \mathrm{m} .$ The electric force on this particle is $2.0 \times 10^{-13} \mathrm{N} .$ What is the speed of such a particle? (The electric force is much greater than the particle's weight, which can be ignored.)

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 71

You probably think of wet surfaces as being slippery. Surprisingly, the opposite is true for human skin, as you can demonstrate by sliding a dry versus a slightly damp fingertip along a smooth surface such as a desktop. Researchers have found that the static coefficient of friction between dry skin and steel is $0.27,$ while that between damp skin and steel can be as high as $1.4 .$ Suppose a man holds a steel rod vertically in his hand, exerting a $400 \mathrm{N}$ grip force on the rod. What is the heaviest rod he can hold without slipping if
a. His hands are dry?
b. His hands are wet?

Supratim Pal

Numerade Educator

Problem 72

Researchers often use force plates to measure the forces that people exert against the floor during movement. A force plate works like a bathroom scale, but it keeps a record of how the reading changes with time. Figure $\mathrm{P} 5.72$ shows the data from a force plate as a woman jumps straight up and then lands.
a. What was the vertical component of her acceleration during push-off?
b. What was the vertical component of her acceleration while in the air?
c. What was the vertical component of her acceleration during the landing?
d. What was her speed as her feet left the force plate?
e. How high did she jump?

Jerrah Biggerstaff

Jerrah Biggerstaff

Numerade Educator

Problem 73

A person with compromised pinch strength in his fingers can only exert a normal force of $6.0 \mathrm{N}$ to either side of a pinch-held object, such as the book shown in Figure P5.73. What is the greatest mass book he can hold onto vertically before it slips out of his fingers? The coefficient of static friction of the surface between the fingers and the book cover is 0.80 .

Sachin Rao

Numerade Educator

Problem 74

It's possible for a determined group of people to pull an aircraft. Drag is negligible at low speeds, and the only force impeding motion is the rolling friction of the rubber tires on the concrete runway. In $2000,$ a team of 60 British police officers set a world record by pulling a Boeing 747 , with a mass of $200,000 \mathrm{kg},$ a distance of $100 \mathrm{m}$ in $53 \mathrm{s}$. The plane started at rest. Estimate the force with which each officer pulled on the plane, assuming constant pulling force and constant acceleration.

Sachin Rao

Numerade Educator

Problem 75

$\mathrm{A} 1.0 \mathrm{~kg}$ ball and a $2.0 \mathrm{~kg}$ ball are connected by a $1.0-\mathrm{~m}$ -long rigid, massless rod. The rod and balls are rotating clockwise about their center of gravity at $20 \mathrm{rpm} .$ What torque will bring the balls to a halt in $5.0 \mathrm{~s} ?$

Meghan Miholics

Meghan Miholics

Numerade Educator

Problem 76

A simple model shows how drawing a bow across a violin string causes the string to vibrate. As the bow moves across the string, static friction between the bow and the string pulls the string along with the bow. At some point, the tension pulling the string back exceeds the maximum static friction force and the string snaps back. This process repeats cyclically, causing the string's vibration. Assume the tension in a 0.33 -m-long violin string is $50 \mathrm{N}$, and the coefficient of static friction between the bow and the string is $\mu_{\mathrm{s}}=0.80 .$ If the normal force of the bow on the string is $0.75 \mathrm{N},$ how far can the string be pulled before it slips if the string is bowed at its center?

Supratim Pal

Numerade Educator

Problem 77

Two blocks are at rest on a frictionless incline, as shown in Figure P5.77. What are the tensions in the two strings?

Sachin Rao

Numerade Educator

Problem 78

Jason works for a moving company. A 45 kg wooden crate is sitting on the wooden ramp of his truck; the ramp is angled at $11^{\circ} .$ What is the magnitude of the force, directed parallel to the ramp, that he needs to exert on the crate to get it to start moving
a. Up the ramp?
b. Down the ramp?

Vishal Gupta

Numerade Educator

Problem 79

Two identical 2.0 kg blocks are stacked as shown in Figure $\mathrm{P} 5.79 .$ The bottom block is free to slide on a frictionless surface. The coefficient of static friction between the blocks is $0.35 .$ What is the maximum horizontal force
that can be applied to the lower block without the upper block slipping?

Sachin Rao

Numerade Educator

Problem 80

Dana loads luggage into an airplane using a conveyor belt tilted at an angle of $20^{\circ} .$ She places a few pieces of luggage on the belt before it starts to move, then she turns the belt on. It takes the belt $0.70 \mathrm{s}$ to reach its top speed of $1.2 \mathrm{m} / \mathrm{s}$. Does the luggage slip? Assume $\mu_{\mathrm{s}}=0.50$ between the luggage and the belt.

Sachin Rao

Numerade Educator

Problem 81

In rock climbing, various rope and pulley systems have been devised to help haul up heavy loads, including injured climbers. A rescuer is hauling up an injured climber who weighs $660 \mathrm{N}$ using the rope and pulley system shown in Figure $\mathrm{P} 5.81$. (The ropes in this figure are drawn at various angles for clarity, but you can assume they're all vertical.)
a. What is the tension in rope $1,$ the rope that the rescuer pulls on?
b. What is the tension in rope $2 ?$

Prabhu Ramji

Numerade Educator

Problem 82

Two blocks are connected by a string as in Figure $\mathrm{P} 5.82$. What is the upper block's acceleration if the coefficient of kinetic friction between the block and the table is $0.20 ?$

Vishal Gupta

Numerade Educator

Problem 83

The ramp in Figure $\mathrm{P} 5.83$ is frictionless. If the blocks are released from rest, which way does the $10 \mathrm{kg}$ block slide, and what is the magnitude of its acceleration?

Sachin Rao

Numerade Educator

Problem 84

The $100 \mathrm{kg}$ block in Figure $\mathrm{P} 5.84$ takes $6.0 \mathrm{s}$ to reach the floor after being released from rest. What is the mass of the block on the left?

Sachin Rao

Numerade Educator

Problem 85

In the winter sport of curling, players give a $20 \mathrm{kg}$ stone a push across a sheet of ice. The stone moves approximately $40 \mathrm{m}$ before coming to rest. The final position of the stone, in principle, only depends on the initial speed at which it is launched and the force of friction between the ice and the stone, but team members can use brooms to sweep the ice in front of the stone to adjust its speed and trajectory a bit; they must do this without touching the stone. Judicious sweeping can lengthen the travel of the stone by $3 \mathrm{m}$.
I A curler pushes a stone to a speed of $3.0 \mathrm{m} / \mathrm{s}$ over a time of $2.0 \mathrm{s}$. Ignoring the force of friction, how much force must the curler apply to the stone to bring it up to speed?
A. $3.0 \mathrm{N}$
B. $15 \mathrm{N}$
C. $30 \mathrm{N}$
D. $150 \mathrm{N}$

Sachin Rao

Numerade Educator

Problem 86

The sweepers in a curling competition adjust the trajectory of the stone by
A. Decreasing the coefficient of friction between the stone and the ice.
B. Increasing the coefficient of friction between the stone and the ice.
C. Changing friction from kinetic to static.
D. Changing friction from static to kinetic.

Sachin Rao

Numerade Educator

Problem 87

Suppose the stone is launched with a speed of $3 \mathrm{m} / \mathrm{s}$ and travels $40 \mathrm{m}$ before coming to rest. What is the approximate magnitude of the friction force on the stone?
A. $0 \mathrm{N}$
B. $2 \mathrm{N}$
C. $20 \mathrm{N}$
D. $200 \mathrm{N}$

Sachin Rao

Numerade Educator

Problem 88

Suppose the stone's mass is increased to $40 \mathrm{kg},$ but it is launched at the same $3 \mathrm{m} / \mathrm{s}$. Which one of the following is true?
A. The stone would now travel a longer distance before coming to rest.
B. The stone would now travel a shorter distance before coming to rest.
C. The coefficient of friction would now be greater
D. The force of friction would now be greater.

Sachin Rao

Numerade Educator